Modeling with Periodic Functions Answers

The period is seconds.

b = pi/2pi2pi

Graph the function using the graphing calculator. Find the least positive value of t at which the pendulum is in the center.t = sec

To the nearest thousandth, find the position of the pendulum when t = 4.25 sec. d = in.

b = pi/20pi/10pi/5

a =

a is the length of the bladeheight of the windmillnumber of rotations per minute.

This amplitude is [___] meters. a = [___]

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. Let t = 0 be 12:00 am.Graph the equation d = -1.5 cosine left-bracket StartFraction 4 pi over 25 EndFraction t right-bracket + 4 that models the situation using a graphing calculator and use it to answer the following questions.

The graph of these points follows a path resembling a .

A graph has month on the x-axis and temperature in degrees Fahrenheit on the y-axis. Month 0 is 23; Month 1 is 35; month 2 is 48; month 3 is 65; month 4 is 74; month 5 is 80; month 6 is 76; month 7 is 64; month 8 is 50; month 9 is 32; month 10 is 24; month 11 is 20. Use the graph to write an equation y = acos[b(x – h)] + k to model the situation.The amplitude is ,

The blades of the windmill turn on an axis that is 5152025 feet from the ground.

The vertical shift, k, is the length of the bladeheight of the windmillnumber of rotations per minute.

This amplitude is [___] meters. a = [___]

At approximately what time on the next day does the depth first reach 4 meters?

so a = .

The blades of the windmill are 5152025 feet long.